Learning the Integral of a Diffusion Model

Flow maps, formalized via Boffi et al.'s taxonomy, train neural networks to directly predict integral mappings between arbitrary points on noise-to-data trajectories, bypassing iterative tangent estimation used in standard diffusion sampling. Unlike distillation methods requiring pretrained teacher models, flow maps support from-scratch training while enabling fewer NFEs, reward-guided generation, and improved steerability. ML researchers optimizing diffusion inference pipelines or fine-tuning with RL-based objectives should prioritize this framework as a structurally cleaner alternative to consistency models and progressive distillation.